### Abstract

A matrix is said to be two-valued if its elements assume at most two different values. We studied the problem of reconstructing a two-valued matrix from its marginals-that is, from its row sums and column sums-but without any knowledge of the value pair on hand. Provided at least one of these marginals is nonconstant, only finitely many (though possibly many) value pairs can lead to a valid reconstruction. Our considerations lead to an efficient algorithm for calculating all possible solutions, each with its own value pair. Special attention is given to uniqueness pairs-that is, value pairs to which there corresponds precisely one matrix having the correct marginals. Unless both marginals are constant, there can be no more than two uniqueness pairs.

Original language | English |
---|---|

Pages (from-to) | 110-117 |

Number of pages | 8 |

Journal | International Journal of Imaging Systems and Technology |

Volume | 9 |

Issue number | 2-3 |

Publication status | Published - 1998 |

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### ASJC Scopus subject areas

- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering
- Atomic and Molecular Physics, and Optics

### Cite this

*International Journal of Imaging Systems and Technology*,

*9*(2-3), 110-117.

**Reconstruction of two-valued matrices from their two projections.** / Kemperman, J. H B; Kuba, A.

Research output: Contribution to journal › Article

*International Journal of Imaging Systems and Technology*, vol. 9, no. 2-3, pp. 110-117.

}

TY - JOUR

T1 - Reconstruction of two-valued matrices from their two projections

AU - Kemperman, J. H B

AU - Kuba, A.

PY - 1998

Y1 - 1998

N2 - A matrix is said to be two-valued if its elements assume at most two different values. We studied the problem of reconstructing a two-valued matrix from its marginals-that is, from its row sums and column sums-but without any knowledge of the value pair on hand. Provided at least one of these marginals is nonconstant, only finitely many (though possibly many) value pairs can lead to a valid reconstruction. Our considerations lead to an efficient algorithm for calculating all possible solutions, each with its own value pair. Special attention is given to uniqueness pairs-that is, value pairs to which there corresponds precisely one matrix having the correct marginals. Unless both marginals are constant, there can be no more than two uniqueness pairs.

AB - A matrix is said to be two-valued if its elements assume at most two different values. We studied the problem of reconstructing a two-valued matrix from its marginals-that is, from its row sums and column sums-but without any knowledge of the value pair on hand. Provided at least one of these marginals is nonconstant, only finitely many (though possibly many) value pairs can lead to a valid reconstruction. Our considerations lead to an efficient algorithm for calculating all possible solutions, each with its own value pair. Special attention is given to uniqueness pairs-that is, value pairs to which there corresponds precisely one matrix having the correct marginals. Unless both marginals are constant, there can be no more than two uniqueness pairs.

UR - http://www.scopus.com/inward/record.url?scp=0031698956&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031698956&partnerID=8YFLogxK

M3 - Article

VL - 9

SP - 110

EP - 117

JO - International Journal of Imaging Systems and Technology

JF - International Journal of Imaging Systems and Technology

SN - 0899-9457

IS - 2-3

ER -